a) Field of the Invention
This invention relates to a reflection type imaging optical system suitable for image formation of light in an X-ray wave band.
b) Description of the Prior Art
As optical systems suitable for image formation of light in an X-ray wave band, a Schwarzshild type optical system combining a concave mirror having an aperture at its center portion with a convex mirror as shown in FIG. 1 and a Walter type optical system compounded of a hyperboloid of revolution and an ellipsoid of revolution as depicted in FIG. 2 are widely known, and some other optical systems are constructed from such three or more mirrors as in FIGS. 3A, 3B and 3C (refer to Appl. Opt. Vol. 18 No. 24, 4185, 1979).
X rays will undergo total reflection when a grazing angle is smaller than a certain angle with respect to various substances. Such an angle is termed a critical angle and depends on optical constants inherent in substances and on wavelengths of rays of light. When the grazing angle of a ray of light is larger than the critical angle, its reflectance will diminish rapidly in the range of wavelengths of an X-ray region. In such an instance, it is known as a provision for the improvement of the reflectance that a multilayer film is formed as lamination on a substrate to utilize the interference of light. The multilayer film has dispersion properties relying on an incident angle (namely, an angle made by the normal of a reflecting surface) of light and on a wavelength of incident light. In some of multilayer films, for example, as shown in FIG. 4A, a pair of layers are formed with two kinds of substances A, B, which are laminated on the substrate by the period of constant thickness. In this case, respective thicknesses d.sub.1, d.sub.2 of the substances A, B are optimized by Fresnel's recurrence formula (Takeshi Namioka, Journal of the Japan Society of Precision Engineering, 52/11/1986, P.1843) so that the reflectance is maximized when light having a wavelength .lambda. is incident on a film surface at an angle .theta..sub.0.
In addition, another example, as depicted in FIG. 4B, shows a multilayer film having a non-periodic structure in which respective thicknesses d.sub.1, d.sub.2 of the substances A, B are not constant (Takeshi Namioka, Kagaku-kenkyuhi Hojokin Kenkyu-seika Hokokusho (1985)).
Where the reflection type imaging optical system is used for the image formation of light in the range of wavelengths of the X-ray region, it is necessary that the surface of a reflecting mirror is coated with the multilayer film to secure desired reflectance.
FIG. 5 is a diagram showing coordinate axes in evaluating the brightness of the reflection type imaging optical system comprising the reflecting mirror coated with the multilayer film and explaining the notation of various signs. In this diagram, a reflecting surface similar to the concave mirror of the Schwarzshild type optical system is shown and its optical axis is taken as a y axis, with an origin at an object point O, followed by an x-z plane normal to the y axis. Angles .theta., .phi. are plotted as in the diagram, the maximum and minimum values of the angle .theta. made by light rays capable of being incident on the imaging optical system, among those emanating from the object point O, are taken as .theta..sub.max and .theta..sub.min, respectively, and an incident angle of light on a j-th reflecting surface from the object point side as .theta..sub.j. In this case, the brightness at an image point I of the imaging optical system is defined, as total transmittance .alpha., by ##EQU1## where Ie: the energy intensity of light emanating from the object point O which traverses a distance at a unit time per unit solid angle,
R.sub.k : the reflectance at a k-th reflecting surface, PA1 .OMEGA.: the solid angle at the object point O subtended by an effective aperture of the optical system, PA1 .theta.: an angle made by the light ray emanating from the object point O with the optical axis (y axis), PA1 .phi.: an angle made by a projecting image, onto the x-z plane, of the light ray passing through the object point O with the z axis when the x and z axes are plotted perpendicular to the optical axis, and PA1 N: the number of reflecting surfaces contained in the imaging optical system. PA1 .DELTA..phi.=2 .pi./n.sub..phi., .DELTA..theta.=2 .pi./n.sub..theta. PA1 n.sub..phi. and n.sub..theta. are integers.
The region of integration is assumed to be in the range (hatched portion) in which the light traverses the effective aperture of the optical system.
Formula (1) can be rewritten as follows: ##EQU2## Here, .theta.j : .theta. min+j.multidot..DELTA..theta.,
where j,
As mentioned above, the multilayer film has dispersion properties relying on the wavelength and the incident angle. As such, unless the multilayer film is designed to coat each reflecting surface with consideration for these properties, sufficient reflectance cannot be derived from each reflecting surface and neither can the brightness (namely, the total transmittance .alpha.) sufficient for an image surface to be secured. In the past, however, an optimized design of the multilayer film coating each reflecting surface has never been considered.